On interpolating sequences for Bloch type spaces

preprint2022arXivOpen access

Abstract

When we deal with H∞H^{\infty}, it is known that c0−c_0-interpolating sequences are interpolating and it is sufficient to interpolate idempotents of ℓ∞\ell_\infty in order to interpolate the whole ℓ∞\ell_\infty. We will extend these results to the frame of interpolating sequences for Bloch type spaces Bv∞\mathcal{B}_{v}^\infty and study the connection between the interpolating operators on Bv∞\mathcal{B}_{v}^\infty and Bv0\mathcal{B}_v^0. Furthermore, for some particular weights vv, we will provide examples of interpolating sequences for Bv∞\mathcal{B}_{v}^\infty whose constant of separation is as close to 0 as desired.

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